If `xdy=ydx+y^2dy` and `y(1)=1`, then `y(-3)` is equal to (A) `1` (B) `5` (C) `4` (D) `3`

If (dy)/(dx)=y+3 " "and" y(0)=2, then " "y(ln2) is equal to : (1) 7 (2) 5 (3) 13 (4) -2

For the primitive integral equation y dx+y^2dy=xdy ; x in R ,y >0,y(1)=1, then y(-3) is (a) 3 (b) 2 (c) 1 (d) 5

If y=y(x) and ((2+sinx)/(y+1))dy/dx=-cosx, y(0)=1 , then y(pi/2) equals (A) 1/3 (B) 2/3 (C) -1/3 (D) 1

Let y(x) be the solution of the differential equation (dy)/(dx)+(3y)/(cos^2x)=1/(cos^2x) and y(pi/4)=4/3 then vaue of y(-pi/4) is equal to (a) -4/3 (b) 1/3 (c) e^6+1/3 (d) 3

If the curve a y+x^2=7 and x^3=y cut orthogonally at (1,\ 1) , then a is equal to (a) 1 (b) -6 (c) 6 (d) 0

tan^(-1)(x/y)-tan^(-1)(x-y)/(x+y) is equal to(A) pi/2 (B) pi/3 (C) pi/4 (D) (-3pi)/4

If a curve y=f(x) passes through the point (1,-1) and satisfies the differential equation ,y(1+x y)dx""=x""dy , then f(-1/2) is equal to: (1) -2/5 (2) -4/5 (3) 2/5 (4) 4/5

tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y)) is equal to (A) pi/2 (B) pi/3 (C) pi/4 (D) (-3pi)/4

If ((2+cosx)/(3+y))(dy)/(dx)+sinx=0 and y(0)=1 , then y((pi)/(3)) is equal to

If y=2x-3 is tangent to the parabola y^2=4a(x-1/3), then a is equal to (a) (22)/3 (b) -1 (c) (14)/3 (d) (-14)/3